The Kalam Cosmological Argument

[Belacqua]

All of them make clear that additional information about that first cause, e.g. that it must be the God of the Bible, are not included in the argument, and must be argued through other means. 

Anselm and Augustine both use it to argue their god. As you point out, that is indeed a non sequitur.

Many Christians use a First Cause argument to show that there is a first cause. 

Of course they think that the first cause is God. However, to show that God could be a first cause requires additional arguments.

It's obvious that the Kalam argument is Muslim. (Kalam is a kind of Islamic medieval Aristotelian theology.) These thinkers thought it applied to the Muslim God. Craig needs additional arguments to show that a Kalam-style first cause argument applies to the Christian God.